We analyze the transport of a point-size Brownian particle under the influence of a constant and uniform force field through a slowly varying periodic channel whose crosssectional area variations represent effective "entropy barriers." Using generalized Taylor-Aris dispersion (macrotransport) theory for spatially periodic media, we compute the mean velocity and effective diffusion coefficient (dispersivity) describing the long-time global transport of the particle. Systematic asymptotic perturbation analysis illuminates the transport process occurring in the strong-field limit, notably the role of the mean-squared channel roughness. The results thus obtained compare favorably with Brownian dynamics simulations over the full range of driving forces.

Over the last two decades, the introduction of new methods such as pulsed-field gel electrophoresis and capillary array electrophoresis has made it possible to map and sequence entire genomes, including our own. The development of these experimental methods has been helped by the progress of theoretical and computational sciences, and the interactions between these three modi operandi of modern science are still pushing the limits of our technologies. We now see a clear trend towards proteomics and microfluidic (even nanofluidic!) devices. In this review, we take a look at the progress of the field over the last 3 years using the glasses of the theoretical scientist and focusing mostly on new ideas and concepts. About a dozen different subfields are discussed and reviewed. We conclude by giving a commented list of some of the best review articles published over the last 2-3 years.

We present a Brownian dynamics model which we use to study the kinetics and thermodynamics of single-stranded DNA hairpins, gaining insights into the role of stem mismatches and the kinetics rates underlying the melting transition. The model is a base-backbone type in which the DNA bases and sugar-phosphate backbone are represented as single units (beads) in the context of the Brownian dynamics simulations. We employ a minimal number of bead-bead interactions, leading to a simple computational scheme. To demonstrate the veracity of our model for DNA hairpins, we show that the model correctly captures the effects of base stacking, hydrogen bonding, and temperature on both the thermodynamics and the kinetics of hairpin formation and melting. When cast in dimensionless form, the thermodynamic results obtained from the present model compare favorably with default predictions of the m-fold server, although the present model is not sufficiently robust to provide dimensional results. The kinetic data at low temperatures indicate frequent but short-lived opening events, consistent with the measured chain end-to-end probability distribution. The model is also used to study the effect of base mismatches in the stem of the hairpin. With the parameters used here, the model overpredicts the relative shift in the melting temperature due to mismatches. The melting transition can be primarily attributed to a rapid increase in the hairpin opening rate rather than an equivalent decrease in the closing rate, in agreement with single-molecule experimental data.

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In this paper, we present a systematic Monte Carlo study of the self-assembly of nonionic, amphiphilic, chainlike molecules in dilute solution. The focus is on the regime in which the molecules form relatively weakly segregated micelles, which are in equilibrium with small submicellar aggregates. We study the size and shape distributions of the aggregates, and the structure of the aggregates’ cores and surfaces. In some cases, spherical micelles, relatively large nonspherical micelles, and submicellar aggregates, all coexist. The size distributions of the spherical micelles are approximately Gaussian, while the nonspherical micelles contribute non-Gaussian tails at relatively large aggregation numbers. The simulation results are interpreted in terms of a simple theory of spherical micelles, and the size distributions are compared with its predictions. For the cases where the agreement is good, we combine the simulations and the theory to calculate the critical micelle concentration as functions of the chain lengths and solvent quality. In cases where there are nonspherical aggregates, the asphericity is quantified using the principal radii of gyration of the micelles, and the size distributions are compared with mean field predictions that account for both spherical and nonspherical aggregates.